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I agree with Quantum. I'd argue that there are huge differences between Ivy League schools and non-Ivy league schools.

If you're child is attending a large state school or an Ivy, chances are that many classes will be taught by TAs. That isn't something that is limited to the Ivys. However, at all institutions, more than half of the faculty is likely to consist of non-tenure track faculty (http://www.aaup.org/issues/contingency/background-facts). If your school is in an area with a lot of unemployed PhDs (such as an area near a large PhD granting institution), chances are that there will be a lot of competition for those poorly paid faculty positions. If your child is attending a rural university without a PhD program, the pickings may be more slim and the quality of the faculty may be lower.

However, I think that the peer group might be even more important than the faculty. Ivy League schools are full of kids with high IQs. Less selective schools are not. I attended a top-10 SLAC where the lowest math class was Calculus. I work at a regional university with average SAT scores in the 1100s and where a lot of students know less math than my elementary school-aged son. There also is a huge difference between the classes at my university and at the one that I attended. At my SLAC, faculty could assume that the students were competent in math and were capable of learning the material on their own. At the school where I teach, I can't make that same assumption. The classes are geared at a lower level, but are probably taught more clearly at my current university. By clearly, I mean that we do not expect our students to make big leaps on their own without guidance. At my current university, we also require our students to do more homework because they 1) do not tend to do well on exams and need the extra points to pass their classes and 2) need the extra reinforcement to understand the material. You can get an idea of whether a school thinks that its gen ed classes are generic or not by looking at whether or not they accept AP scores. If they don't accept them, they think that their classes offer something extra that is not found in a typical gen ed class.

Would I send my DYS-qualifying daughter to my current university? Yes, because she'll get a huge tuition break. She'll also be a big fish in a small pond. Studies have shown that the top students at a particular university tend to drift toward STEM careers, so she is probably more likely to go into a STEM field if she attends this school versus an Ivy. Would she receive a better education at an Ivy? Probably.